# How smooth is almost every function in a Sobolev space?

Aurélia Fraysse; Stéphane Jaffard

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 2, page 663-682
- ISSN: 0213-2230

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topFraysse, Aurélia, and Jaffard, Stéphane. "How smooth is almost every function in a Sobolev space?." Revista Matemática Iberoamericana 22.2 (2006): 663-682. <http://eudml.org/doc/41987>.

@article{Fraysse2006,

abstract = {We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.},

author = {Fraysse, Aurélia, Jaffard, Stéphane},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacios de funciones lineales; Espacios de Sobolev; Espacios de Besov; Continuidad; Regularidad; Fractales; Dimensión de Hausdorff; Ondículas; Sobolev spaces; Besov spaces; prevalence; Haar-null sets; multifractal functions; Hölder regularity; Hausdorff dimension; wavelet bases},

language = {eng},

number = {2},

pages = {663-682},

title = {How smooth is almost every function in a Sobolev space?},

url = {http://eudml.org/doc/41987},

volume = {22},

year = {2006},

}

TY - JOUR

AU - Fraysse, Aurélia

AU - Jaffard, Stéphane

TI - How smooth is almost every function in a Sobolev space?

JO - Revista Matemática Iberoamericana

PY - 2006

VL - 22

IS - 2

SP - 663

EP - 682

AB - We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

LA - eng

KW - Espacios de funciones lineales; Espacios de Sobolev; Espacios de Besov; Continuidad; Regularidad; Fractales; Dimensión de Hausdorff; Ondículas; Sobolev spaces; Besov spaces; prevalence; Haar-null sets; multifractal functions; Hölder regularity; Hausdorff dimension; wavelet bases

UR - http://eudml.org/doc/41987

ER -

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